TSTP Solution File: KRS143+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KRS143+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 02:56:41 EDT 2022
% Result : Theorem 2.66s 1.36s
% Output : Proof 4.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KRS143+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 7 05:32:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.53/0.60 ____ _
% 0.53/0.60 ___ / __ \_____(_)___ ________ __________
% 0.53/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.60
% 0.53/0.60 A Theorem Prover for First-Order Logic
% 0.53/0.60 (ePrincess v.1.0)
% 0.53/0.60
% 0.53/0.60 (c) Philipp Rümmer, 2009-2015
% 0.53/0.60 (c) Peter Backeman, 2014-2015
% 0.53/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.60 Bug reports to peter@backeman.se
% 0.53/0.60
% 0.53/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.60
% 0.53/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.41/0.93 Prover 0: Preprocessing ...
% 1.75/1.03 Prover 0: Warning: ignoring some quantifiers
% 1.75/1.04 Prover 0: Constructing countermodel ...
% 1.86/1.13 Prover 0: gave up
% 1.86/1.13 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.86/1.15 Prover 1: Preprocessing ...
% 2.46/1.26 Prover 1: Constructing countermodel ...
% 2.66/1.35 Prover 1: proved (223ms)
% 2.66/1.35
% 2.66/1.36 No countermodel exists, formula is valid
% 2.66/1.36 % SZS status Theorem for theBenchmark
% 2.66/1.36
% 2.66/1.36 Generating proof ... found it (size 47)
% 3.51/1.59
% 3.51/1.59 % SZS output start Proof for theBenchmark
% 3.51/1.59 Assumed formulas after preprocessing and simplification:
% 3.51/1.59 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (rp(v9, v8) = v7) | ~ (rp(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (rp(v6, v8) = 0) | ~ (rp(v6, v7) = 0) | ~ (cc(v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (rp(v7, v6) = v8) | ~ (rp(v7, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (rp(v6, v7) = v8) | ~ (rp(v6, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (xsd_string(v8) = v7) | ~ (xsd_string(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (xsd_integer(v8) = v7) | ~ (xsd_integer(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (cowlThing(v8) = v7) | ~ (cowlThing(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (cowlNothing(v8) = v7) | ~ (cowlNothing(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (cc(v8) = v7) | ~ (cc(v8) = v6)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (xsd_string(v6) = v7) | ~ (xsd_string(v6) = 0)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (xsd_string(v6) = v7) | xsd_integer(v6) = 0) & ! [v6] : ! [v7] : (v7 = 0 | ~ (xsd_integer(v6) = v7) | ~ (xsd_integer(v6) = 0)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (cowlThing(v6) = v7) | ~ (cowlThing(v6) = 0)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (cowlThing(v6) = v7)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (cowlNothing(v6) = v7) | ~ (cowlNothing(v6) = 0)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (cc(v6) = v7) | ~ (cc(v6) = 0)) & ! [v6] : ( ~ (xsd_string(v6) = 0) | ? [v7] : ( ~ (v7 = 0) & xsd_integer(v6) = v7)) & ! [v6] : ~ (cowlNothing(v6) = 0) & ! [v6] : ( ~ (cc(v6) = 0) | ? [v7] : rp(v6, v7) = 0) & ((v1 = 0 & cc(v0) = 0 & ( ! [v6] : ~ (rp(v0, v6) = 0) | (v5 = 0 & v4 = 0 & ~ (v3 = v2) & rp(v0, v3) = 0 & rp(v0, v2) = 0))) | (xsd_string(v0) = v1 & xsd_integer(v0) = v2 & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0)))) | (cowlThing(v0) = v1 & cowlNothing(v0) = v2 & ( ~ (v1 = 0) | v2 = 0))))
% 3.86/1.64 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 3.86/1.64 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | ~ (cc(v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v1, v0) = v2) | ~ (rp(v1, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v0, v1) = v2) | ~ (rp(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cc(v2) = v1) | ~ (cc(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cc(v0) = v1) | ~ (cc(v0) = 0)) & ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) & ! [v0] : ~ (cowlNothing(v0) = 0) & ! [v0] : ( ~ (cc(v0) = 0) | ? [v1] : rp(v0, v1) = 0) & ((all_0_4_4 = 0 & cc(all_0_5_5) = 0 & ( ! [v0] : ~ (rp(all_0_5_5, v0) = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & ~ (all_0_2_2 = all_0_3_3) & rp(all_0_5_5, all_0_2_2) = 0 & rp(all_0_5_5, all_0_3_3) = 0))) | (xsd_string(all_0_5_5) = all_0_4_4 & xsd_integer(all_0_5_5) = all_0_3_3 & ((all_0_3_3 = 0 & all_0_4_4 = 0) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0)))) | (cowlThing(all_0_5_5) = all_0_4_4 & cowlNothing(all_0_5_5) = all_0_3_3 & ( ~ (all_0_4_4 = 0) | all_0_3_3 = 0)))
% 3.86/1.66 |
% 3.86/1.66 | Applying alpha-rule on (1) yields:
% 3.86/1.66 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 3.86/1.66 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | ~ (cc(v0) = 0))
% 3.86/1.66 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0))
% 3.86/1.66 | (5) (all_0_4_4 = 0 & cc(all_0_5_5) = 0 & ( ! [v0] : ~ (rp(all_0_5_5, v0) = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & ~ (all_0_2_2 = all_0_3_3) & rp(all_0_5_5, all_0_2_2) = 0 & rp(all_0_5_5, all_0_3_3) = 0))) | (xsd_string(all_0_5_5) = all_0_4_4 & xsd_integer(all_0_5_5) = all_0_3_3 & ((all_0_3_3 = 0 & all_0_4_4 = 0) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0)))) | (cowlThing(all_0_5_5) = all_0_4_4 & cowlNothing(all_0_5_5) = all_0_3_3 & ( ~ (all_0_4_4 = 0) | all_0_3_3 = 0))
% 3.86/1.66 | (6) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 3.86/1.66 | (7) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1))
% 3.86/1.66 | (8) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0))
% 3.86/1.66 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0))
% 3.86/1.67 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0))
% 3.86/1.67 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0))
% 3.86/1.67 | (12) ! [v0] : ~ (cowlNothing(v0) = 0)
% 3.86/1.67 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (cc(v0) = v1) | ~ (cc(v0) = 0))
% 3.86/1.67 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0))
% 3.86/1.67 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v0, v1) = v2) | ~ (rp(v0, v1) = 0))
% 3.86/1.67 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cc(v2) = v1) | ~ (cc(v2) = v0))
% 3.86/1.67 | (17) ! [v0] : ( ~ (cc(v0) = 0) | ? [v1] : rp(v0, v1) = 0)
% 3.86/1.67 | (18) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0)
% 3.86/1.67 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v1, v0) = v2) | ~ (rp(v1, v0) = 0))
% 3.86/1.67 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0))
% 3.86/1.67 | (21) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0))
% 3.86/1.67 |
% 3.86/1.67 +-Applying beta-rule and splitting (5), into two cases.
% 3.86/1.67 |-Branch one:
% 3.86/1.67 | (22) (all_0_4_4 = 0 & cc(all_0_5_5) = 0 & ( ! [v0] : ~ (rp(all_0_5_5, v0) = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & ~ (all_0_2_2 = all_0_3_3) & rp(all_0_5_5, all_0_2_2) = 0 & rp(all_0_5_5, all_0_3_3) = 0))) | (xsd_string(all_0_5_5) = all_0_4_4 & xsd_integer(all_0_5_5) = all_0_3_3 & ((all_0_3_3 = 0 & all_0_4_4 = 0) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0))))
% 3.86/1.68 |
% 3.86/1.68 +-Applying beta-rule and splitting (22), into two cases.
% 3.86/1.68 |-Branch one:
% 3.86/1.68 | (23) all_0_4_4 = 0 & cc(all_0_5_5) = 0 & ( ! [v0] : ~ (rp(all_0_5_5, v0) = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & ~ (all_0_2_2 = all_0_3_3) & rp(all_0_5_5, all_0_2_2) = 0 & rp(all_0_5_5, all_0_3_3) = 0))
% 3.86/1.68 |
% 3.86/1.68 | Applying alpha-rule on (23) yields:
% 3.86/1.68 | (24) all_0_4_4 = 0
% 3.86/1.68 | (25) cc(all_0_5_5) = 0
% 3.86/1.68 | (26) ! [v0] : ~ (rp(all_0_5_5, v0) = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & ~ (all_0_2_2 = all_0_3_3) & rp(all_0_5_5, all_0_2_2) = 0 & rp(all_0_5_5, all_0_3_3) = 0)
% 3.86/1.68 |
% 3.86/1.68 | Instantiating formula (17) with all_0_5_5 and discharging atoms cc(all_0_5_5) = 0, yields:
% 4.11/1.68 | (27) ? [v0] : rp(all_0_5_5, v0) = 0
% 4.11/1.68 |
% 4.11/1.68 | Instantiating (27) with all_11_0_6 yields:
% 4.11/1.68 | (28) rp(all_0_5_5, all_11_0_6) = 0
% 4.11/1.68 |
% 4.11/1.68 +-Applying beta-rule and splitting (26), into two cases.
% 4.11/1.68 |-Branch one:
% 4.11/1.68 | (29) ! [v0] : ~ (rp(all_0_5_5, v0) = 0)
% 4.11/1.68 |
% 4.11/1.68 | Instantiating formula (29) with all_11_0_6 and discharging atoms rp(all_0_5_5, all_11_0_6) = 0, yields:
% 4.11/1.68 | (30) $false
% 4.11/1.68 |
% 4.11/1.68 |-The branch is then unsatisfiable
% 4.11/1.68 |-Branch two:
% 4.11/1.68 | (31) all_0_0_0 = 0 & all_0_1_1 = 0 & ~ (all_0_2_2 = all_0_3_3) & rp(all_0_5_5, all_0_2_2) = 0 & rp(all_0_5_5, all_0_3_3) = 0
% 4.11/1.68 |
% 4.11/1.68 | Applying alpha-rule on (31) yields:
% 4.11/1.68 | (32) rp(all_0_5_5, all_0_3_3) = 0
% 4.11/1.69 | (33) ~ (all_0_2_2 = all_0_3_3)
% 4.11/1.69 | (34) all_0_0_0 = 0
% 4.11/1.69 | (35) rp(all_0_5_5, all_0_2_2) = 0
% 4.11/1.69 | (36) all_0_1_1 = 0
% 4.11/1.69 |
% 4.11/1.69 | Instantiating formula (3) with all_0_2_2, all_11_0_6, all_0_5_5 and discharging atoms rp(all_0_5_5, all_11_0_6) = 0, rp(all_0_5_5, all_0_2_2) = 0, cc(all_0_5_5) = 0, yields:
% 4.11/1.69 | (37) all_11_0_6 = all_0_2_2
% 4.11/1.69 |
% 4.11/1.69 | Instantiating formula (3) with all_0_3_3, all_11_0_6, all_0_5_5 and discharging atoms rp(all_0_5_5, all_11_0_6) = 0, rp(all_0_5_5, all_0_3_3) = 0, cc(all_0_5_5) = 0, yields:
% 4.11/1.69 | (38) all_11_0_6 = all_0_3_3
% 4.11/1.69 |
% 4.11/1.69 | Combining equations (38,37) yields a new equation:
% 4.11/1.69 | (39) all_0_2_2 = all_0_3_3
% 4.11/1.69 |
% 4.11/1.69 | Equations (39) can reduce 33 to:
% 4.11/1.69 | (40) $false
% 4.11/1.69 |
% 4.11/1.69 |-The branch is then unsatisfiable
% 4.11/1.69 |-Branch two:
% 4.11/1.69 | (41) xsd_string(all_0_5_5) = all_0_4_4 & xsd_integer(all_0_5_5) = all_0_3_3 & ((all_0_3_3 = 0 & all_0_4_4 = 0) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0)))
% 4.11/1.69 |
% 4.11/1.69 | Applying alpha-rule on (41) yields:
% 4.11/1.69 | (42) xsd_string(all_0_5_5) = all_0_4_4
% 4.11/1.69 | (43) xsd_integer(all_0_5_5) = all_0_3_3
% 4.11/1.69 | (44) (all_0_3_3 = 0 & all_0_4_4 = 0) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0))
% 4.11/1.69 |
% 4.11/1.69 | Instantiating formula (6) with all_0_5_5 yields:
% 4.11/1.69 | (45) ~ (xsd_string(all_0_5_5) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_5_5) = v0)
% 4.11/1.69 |
% 4.11/1.69 | Instantiating formula (18) with all_0_4_4, all_0_5_5 and discharging atoms xsd_string(all_0_5_5) = all_0_4_4, yields:
% 4.11/1.69 | (46) all_0_4_4 = 0 | xsd_integer(all_0_5_5) = 0
% 4.11/1.69 |
% 4.11/1.69 +-Applying beta-rule and splitting (44), into two cases.
% 4.11/1.69 |-Branch one:
% 4.11/1.69 | (47) all_0_3_3 = 0 & all_0_4_4 = 0
% 4.11/1.70 |
% 4.11/1.70 | Applying alpha-rule on (47) yields:
% 4.11/1.70 | (48) all_0_3_3 = 0
% 4.11/1.70 | (24) all_0_4_4 = 0
% 4.11/1.70 |
% 4.11/1.70 | From (24) and (42) follows:
% 4.11/1.70 | (50) xsd_string(all_0_5_5) = 0
% 4.11/1.70 |
% 4.11/1.70 | From (48) and (43) follows:
% 4.11/1.70 | (51) xsd_integer(all_0_5_5) = 0
% 4.11/1.70 |
% 4.11/1.70 +-Applying beta-rule and splitting (45), into two cases.
% 4.11/1.70 |-Branch one:
% 4.11/1.70 | (52) ~ (xsd_string(all_0_5_5) = 0)
% 4.11/1.70 |
% 4.11/1.70 | Using (50) and (52) yields:
% 4.11/1.70 | (30) $false
% 4.11/1.70 |
% 4.11/1.70 |-The branch is then unsatisfiable
% 4.11/1.70 |-Branch two:
% 4.11/1.70 | (50) xsd_string(all_0_5_5) = 0
% 4.11/1.70 | (55) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_5_5) = v0)
% 4.11/1.70 |
% 4.11/1.70 | Instantiating (55) with all_17_0_7 yields:
% 4.11/1.70 | (56) ~ (all_17_0_7 = 0) & xsd_integer(all_0_5_5) = all_17_0_7
% 4.11/1.70 |
% 4.11/1.70 | Applying alpha-rule on (56) yields:
% 4.11/1.70 | (57) ~ (all_17_0_7 = 0)
% 4.11/1.70 | (58) xsd_integer(all_0_5_5) = all_17_0_7
% 4.11/1.70 |
% 4.11/1.70 | Instantiating formula (2) with all_0_5_5, 0, all_17_0_7 and discharging atoms xsd_integer(all_0_5_5) = all_17_0_7, xsd_integer(all_0_5_5) = 0, yields:
% 4.11/1.70 | (59) all_17_0_7 = 0
% 4.11/1.70 |
% 4.11/1.70 | Equations (59) can reduce 57 to:
% 4.11/1.70 | (40) $false
% 4.11/1.70 |
% 4.11/1.70 |-The branch is then unsatisfiable
% 4.11/1.70 |-Branch two:
% 4.11/1.70 | (61) ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0)
% 4.11/1.71 |
% 4.11/1.71 | Applying alpha-rule on (61) yields:
% 4.11/1.71 | (62) ~ (all_0_3_3 = 0)
% 4.11/1.71 | (63) ~ (all_0_4_4 = 0)
% 4.11/1.71 |
% 4.11/1.71 +-Applying beta-rule and splitting (46), into two cases.
% 4.11/1.71 |-Branch one:
% 4.11/1.71 | (51) xsd_integer(all_0_5_5) = 0
% 4.11/1.71 |
% 4.11/1.71 | Instantiating formula (2) with all_0_5_5, 0, all_0_3_3 and discharging atoms xsd_integer(all_0_5_5) = all_0_3_3, xsd_integer(all_0_5_5) = 0, yields:
% 4.11/1.71 | (48) all_0_3_3 = 0
% 4.11/1.71 |
% 4.11/1.71 | Equations (48) can reduce 62 to:
% 4.11/1.71 | (40) $false
% 4.11/1.71 |
% 4.11/1.71 |-The branch is then unsatisfiable
% 4.11/1.71 |-Branch two:
% 4.11/1.71 | (67) ~ (xsd_integer(all_0_5_5) = 0)
% 4.11/1.71 | (24) all_0_4_4 = 0
% 4.11/1.71 |
% 4.11/1.71 | Equations (24) can reduce 63 to:
% 4.11/1.71 | (40) $false
% 4.11/1.71 |
% 4.11/1.71 |-The branch is then unsatisfiable
% 4.11/1.71 |-Branch two:
% 4.11/1.71 | (70) cowlThing(all_0_5_5) = all_0_4_4 & cowlNothing(all_0_5_5) = all_0_3_3 & ( ~ (all_0_4_4 = 0) | all_0_3_3 = 0)
% 4.11/1.71 |
% 4.11/1.71 | Applying alpha-rule on (70) yields:
% 4.11/1.71 | (71) cowlThing(all_0_5_5) = all_0_4_4
% 4.11/1.71 | (72) cowlNothing(all_0_5_5) = all_0_3_3
% 4.11/1.71 | (73) ~ (all_0_4_4 = 0) | all_0_3_3 = 0
% 4.11/1.71 |
% 4.11/1.71 | Instantiating formula (7) with all_0_4_4, all_0_5_5 and discharging atoms cowlThing(all_0_5_5) = all_0_4_4, yields:
% 4.11/1.71 | (24) all_0_4_4 = 0
% 4.11/1.71 |
% 4.11/1.71 | Instantiating formula (12) with all_0_5_5 yields:
% 4.11/1.71 | (75) ~ (cowlNothing(all_0_5_5) = 0)
% 4.11/1.71 |
% 4.11/1.71 +-Applying beta-rule and splitting (73), into two cases.
% 4.11/1.71 |-Branch one:
% 4.11/1.71 | (63) ~ (all_0_4_4 = 0)
% 4.11/1.71 |
% 4.11/1.71 | Equations (24) can reduce 63 to:
% 4.11/1.71 | (40) $false
% 4.11/1.71 |
% 4.11/1.71 |-The branch is then unsatisfiable
% 4.11/1.71 |-Branch two:
% 4.11/1.71 | (24) all_0_4_4 = 0
% 4.11/1.71 | (48) all_0_3_3 = 0
% 4.11/1.71 |
% 4.11/1.71 | From (48) and (72) follows:
% 4.11/1.71 | (80) cowlNothing(all_0_5_5) = 0
% 4.11/1.71 |
% 4.11/1.71 | Using (80) and (75) yields:
% 4.11/1.71 | (30) $false
% 4.11/1.71 |
% 4.11/1.71 |-The branch is then unsatisfiable
% 4.11/1.71 % SZS output end Proof for theBenchmark
% 4.11/1.71
% 4.11/1.71 1103ms
%------------------------------------------------------------------------------